Problem: Simplify the following expression: $ q = \dfrac{7}{8} - \dfrac{k + 2}{-7} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-7}{-7}$ $ \dfrac{7}{8} \times \dfrac{-7}{-7} = \dfrac{-49}{-56} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{k + 2}{-7} \times \dfrac{8}{8} = \dfrac{8k + 16}{-56} $ Therefore $ q = \dfrac{-49}{-56} - \dfrac{8k + 16}{-56} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-49 - (8k + 16) }{-56} $ Distribute the negative sign: $q = \dfrac{-49 - 8k - 16}{-56}$ $q = \dfrac{-8k - 65}{-56}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{8k + 65}{56}$